3(2x+6)-5(x+8)x=-22

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Solution for 3(2x+6)-5(x+8)x=-22 equation: 


Simplifying
3(2x + 6) + -5(x + 8) * x = -22

Reorder the terms:
3(6 + 2x) + -5(x + 8) * x = -22
(6 * 3 + 2x * 3) + -5(x + 8) * x = -22
(18 + 6x) + -5(x + 8) * x = -22

Reorder the terms:
18 + 6x + -5(8 + x) * x = -22

Reorder the terms for easier multiplication:
18 + 6x + -5x(8 + x) = -22
18 + 6x + (8 * -5x + x * -5x) = -22
18 + 6x + (-40x + -5x2) = -22

Combine like terms: 6x + -40x = -34x
18 + -34x + -5x2 = -22

Solving
18 + -34x + -5x2 = -22

Solving for variable 'x'.

Reorder the terms:
18 + 22 + -34x + -5x2 = -22 + 22

Combine like terms: 18 + 22 = 40
40 + -34x + -5x2 = -22 + 22

Combine like terms: -22 + 22 = 0
40 + -34x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-8 + 6.8x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 6.8x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 6.8x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 6.8x + x2 = 0 + 8
6.8x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
6.8x + x2 = 8

The x term is 6.8x.  Take half its coefficient (3.4).
Square it (11.56) and add it to both sides.

Add '11.56' to each side of the equation.
6.8x + 11.56 + x2 = 8 + 11.56

Reorder the terms:
11.56 + 6.8x + x2 = 8 + 11.56

Combine like terms: 8 + 11.56 = 19.56
11.56 + 6.8x + x2 = 19.56

Factor a perfect square on the left side:
(x + 3.4)(x + 3.4) = 19.56

Calculate the square root of the right side: 4.422668877

Break this problem into two subproblems by setting 
(x + 3.4) equal to 4.422668877 and -4.422668877.


Subproblem 1
x + 3.4 = 4.422668877

Simplifying
x + 3.4 = 4.422668877

Reorder the terms:
3.4 + x = 4.422668877

Solving
3.4 + x = 4.422668877

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.4' to each side of the equation.
3.4 + -3.4 + x = 4.422668877 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
0.0 + x = 4.422668877 + -3.4
x = 4.422668877 + -3.4

Combine like terms: 4.422668877 + -3.4 = 1.022668877
x = 1.022668877

Simplifying
x = 1.022668877


Subproblem 2
x + 3.4 = -4.422668877

Simplifying
x + 3.4 = -4.422668877

Reorder the terms:
3.4 + x = -4.422668877

Solving
3.4 + x = -4.422668877

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.4' to each side of the equation.
3.4 + -3.4 + x = -4.422668877 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
0.0 + x = -4.422668877 + -3.4
x = -4.422668877 + -3.4

Combine like terms: -4.422668877 + -3.4 = -7.822668877
x = -7.822668877

Simplifying
x = -7.822668877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.022668877, -7.822668877}

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